# Math Help - Can anyone help me with this prob?

1. ## Can anyone help me with this prob?

Let $U\subseteq R^n$ be an open set if $\forall x\in U$ there exists an r > 0 such that B(x,r) $\subseteq U$. B(x.r) meaning a ball centered on x with radius r.

1) Let a $\in R^n$. Prove that for all $\epsilon > 0$ B(a, $\epsilon$) is open

2) Show that if $U_1, .... ,U_n$ are open in $R^n$ then $U_1\cap ..... \cap U_n$ also open

2. Anyone?